Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in JAVA):

Solution:
import java.util.*;


public class Main
{
    public static void main( String[] args )
    {
        Scanner in = new Scanner( System.in );
        int n = in.nextInt();
        boolean yes = false;
        for ( int i = 1; i * ( i + 1 ) <= n; i++ )
        {
            int b = n * 2 - i * ( i + 1 );
            int left = 1;
            int right = ( int ) Math.sqrt( b ) + 1;
            while ( left < right )
            {
                int mid = ( left + right ) >> 1;
                if ( mid * ( mid + 1 ) == b ) { yes = true; break; }
                if ( mid * ( mid + 1 ) > b ) right = mid;
                else left = mid + 1;
            }
            if ( yes ) break;
        }
        if ( yes ) System.out.print( "YES" );
        else System.out.print( "NO" );
    }
}